Lecture 10: Work & Energy

Questions of Yesterday1) A student pushes her physics book across a flat table.

Another student pushes his physics book up a 30o inclined plane. Assuming the coefficient of kinetic friction is the same in both cases, in which case is the force of friction acting on the book greater?a) the book on the flat tableb) the book on the inclined planec) the force of friction is the same in both cases

2) If you hold your physics book up against the chalkboard, in what direction is the force of friction directed?a) upwards

b) downwardsc) away from the chalkboardd) into the chalkboard

WorkWe often apply FORCE to an object because we want to

move it from one point to another

WORK is done on an object when… a FORCE is applied to the object while

moving that object through a certain DISPLACEMENT

F

x

W = Fx

Work

F

x

W = FxUnits = N*m = Joule

Magnitude of F * Magnitude of x

ONLY valid if F and x are in the SAME DIRECTION!!

Work is a SCALAR - NO direction!

What about the directions of F and x ??

Work

Fx

W = (Fcosx

Will the same work be done if F is applied in different directions?

Only the component of force in the same direction as the displacement does work on the object!!

F

Work

F

What force is needed to raise the box to the table at

a constant velocity?

How much work do you do when you lift it

to the table? 2 m

10 kg

10 kg

W = (Fcosx

Work

What force is needed to lower

the box from the table to the ground

at a constant velocity?

How much work do you do when you lower it

to the ground?2 m

10 kg

10 kg

W = (Fcosx

Work

Negative work is done on an object when the force is in

the opposite direction to the displacement

2 m

10 kg

10 kg

W = (Fcosx

Work

10 m10 kg 10 kg

W = (Fcosx

What force is needed to carry the box horizontally to

the table at constant velocity?

How much work do you carrying it to the table?

Work

NO WORK is done on the object if the

applied force is perpendicular to the

displacement!

NO component of force is in direction of displacement

10 m10 kg 10 kg

W = (Fcosx

Work-Energy Theorem

Newton’s 2nd Law (∑F = ma) can be difficult to solve when many forces are acting on an object in many

different directions….

The scalar quantity WORK can tell us information about the net force acting on an object and its

induced motion

Wnet = Fnetx = (ma)x

v2 = v02 +

2ax

Wnet = (1/2)mv2 - (1/2)mv02

Work-Energy Theorem

Wnet = (1/2)mv2 - (1/2)mv02

KINETIC ENERGYthe energy of an object

associated with its motion

Units = kg*m2/s2 = Joules (J)

Kinetic Energy KEof an object with mass m moving with a speed v

KE = (1/2)mv2

The total work done on an object is equal to the change in the object’s kinetic energy

Wnet = KEf - KEi =

KE

WORK-ENERGYTHEOREM

Conservative Forces

What work does gravity do on the ball (mass = m)

from 1-2?

The energy lost from 1-2 is regained in 2-3The work done against gravity from 1-2 is recovered in

2-3

Wnet = KEf - KEi = KE

v0

2

31From 2-3?

From 1-3?

Gravity caused NO change in energy over entire trip!

h

Conservative Forces

Gravity is aConservative Force

The energy lost from 1-2 is regained in 2-3The work done against gravity from 1-2 is recovered in

2-3

Wnet = KEf - KEi = KE

v0

2

31

Gravity caused NO change in energy over entire trip!

h

Conservative Forces

A force is conservative if the work it does moving an object between two points is the same no matter what

path taken

Would the work done from 1-3 be different in this case? What about 1-2? 2-3?

Wnet = KEf - KEi = KE

v0

2

31

h

Nonconservative Forces

Friction is a Nonconservative ForceEnergy lost from friction is NOT recovered

The coefficient of kinetic friction between the box and table is k

What work does friction do on the box from 1-4?

What about over the

path 1-2-3-4?

What about 1-2-3-4-1?

Wnet = KEf - KEi = KE

m m

m m

x1

4

2

3

Work done by Friction

Friction causes an object to lose energy in the form of heat

and noise

Friction always acts in a direction opposite an

object’s motion.

Work done by friction is always Negative

Wnet = KEf - KEi = KE

m m

m m

x1

4

2

3

Work done by Friction

What is the work done by each of the forces?

M

A block slides down the inclined plane at a constant velocity.What forces are acting on the block along the incline?

Md

Wnc + Wc = KEf - KEi = KE

What is the net work Wnet done on the block over the distance d?

Practice ProblemA 70-kg runner begins his slide into second base when he is moving at a speed of 4.0 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that

his speed is zero just as he reaches the base.

How much kinetic energy is lost due to friction acting on the runner?

How far does he slide?

Questions of the Day1) You slam on your brakes in a panic and skid a certain

distance d down a straight and level road before coming to a stop. If you had been traveling twice as fast, what would the skidding distance be? a) 2d

b) d/2c) 4dd) d/4

2) As a pendulum swings back and forth, the forces acting on the pendulum are the force of gravity and tension in the supporting cord. Which of these forces does no work on the pendulum?a) Gravityb) Tensionc) neither one does work on the pendulumd) they both do work on the pendulum